हिंदी

Construct the truth table of the following: [(p ∧ q) ∨ r] ∧ [∼r ∨ (p ∧ q)] - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Construct the truth table of the following:

[(p ∧ q) ∨ r] ∧ [∼r ∨ (p ∧ q)]

योग
Advertisements

उत्तर

p q r p∧q (p∧q) ∨ r ∼r ∼r ∨ (p∧q) [(p∧q) ∨ r] ∧ [∼r ∨ (p∧q)]
T T T T T F T T
T T F T T T T T
T F T F T F F F
T F F F F T T F
F T T F T F F F
F T F F F T T F
F F T F T F F F
F F F F F T T F
shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३३]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
अध्याय 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 6.4 | पृष्ठ ३३

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Write the following compound statement symbolically.

If ΔABC is right-angled at B, then m∠A + m∠C = 90°.


Write the following compound statement symbolically.

x is not irrational number but is a square of an integer.


Construct the truth table of the following statement pattern.

(p ∧ q) ↔ (q ∨ r)


If p ∧ q is false and p ∨ q is true, then ______ is not true.


Construct the truth table of the following:

(∼p ∨ ∼q) ↔ [∼(p ∧ q)]


Express the following statement in symbolic form.

Milk is white or grass is green.


Write the truth value of the following statement.

16 is an even number and 8 is a perfect square.


Write the truth value of the following statement.

A quadratic equation has two distinct roots or 6 has three prime factors.


Write the negation of the following statement.

It is false that Nagpur is capital of Maharashtra


Write the following statement in symbolic form.

It is not true that “i” is a real number.


Write the following statement in symbolic form.

Stock prices are high if and only if stocks are rising.


Find the truth value of the following statement.

If a joint venture is a temporary partnership, then discount on purchase is credited to the supplier.


If p and q are true and r and s are false, find the truth value of the following compound statement.

p ∧ (q ∧ r)


If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement:

p ↔ ~ q


Fill in the blanks :

Conjunction of two statement p and q is symbolically written as ______.


State whether the following statement is True or False:

The negation of 10 + 20 = 30 is, it is false that 10 + 20 ≠ 30.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

Mona likes Mathematics and Physics.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

To be brave is necessary and sufficient condition to climb the Mount Everest.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

x3 + y3 = (x + y)3 if xy = 0.


Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.
p→(q ∨ r)


Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

p → q


Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

(p ∧ q) ∧ ∼ r


Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)

If price increases, then demand falls.


Assuming the following statement.

p : Stock prices are high.

q : Stocks are rising.

to be true, find the truth value of the following.

Stock prices are high or stocks are not rising iff stocks are rising.


Write the negation of the following statement.

7 is prime number and Tajmahal is in Agra.


The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.


Find the negation of 10 + 20 = 30


Write the following statements in symbolic form

If Kutab – Minar is in Delhi then Taj - Mahal is in Agra


Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r)


Choose the correct alternative:

Negation of p → (p ˅ ~q) is


State whether the following statement is True or False:

The converse of inverse of ~ p → q is q → ~ p


Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”


Write the following statements in symbolic form.

If Qutub – Minar is in Delhi then Taj-Mahal is in Agra


If p : Every natural number is a real number.
q : Every integer is a complex number. Then truth values of p → q and p ↔ q are ______ and ______ respectively.


If c denotes the contradiction then the dual of the compound statement ∼p ∧ (q ∨ c) is ______ 


Which of the following is false?


Let p : 7 is not greater than 4 and q : Paris is in France by two statements. Then ∼(p ∨ q) is the statement ______ 


Which of the following is NOT true for p → q.


The negation of ∼s ∨ (∼r ∧ s) is equivalent to ______


Conditional of p → q is equivalent to p → ∼ q.


Converse of the statement q `rightarrow` p is ______.


Write the following statement in symbolic form.

It is not true that `sqrt(2)` is a rational number.


Express the following compound statement symbolically:

Delhi is in India but Dhaka is not in Sri Lanka


Construct the truth table for the statement pattern:

[(p → q) ∧ q] → p


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×